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Ross H***berger's love of mathematics comes through very clearly

in From Erd?s to Kiev. He presents intriguing, stimulating problems

that can be solved with elementary mathematical techniques. It will

give pleasure to motivated students and their teachers, but it will

also appeal to anyone who enjoys a mathematical challenge. Most of

the problems in the collection have appeared on national or

international Olympiads or other contests. Thus, they are quite

challenging (with soluti*** that are all the more rewarding). The

soluti*** use straightforward arguments from elementary mathematics

(often not very technical arguments) with only the occasional foray

into sophisticated or advanced ideas. Anyone familia***ith

elementary mathematics can appreciate a large part of the book. The

problems included in this collection are taken from geometry,

number theory, probability, and combinatorics. Soluti*** to the

problems are included.

1. Seven soluti*** Ge***e Evagelopoulos

2. A decomposition of a ***

3. AIME - 1987

4. A problem from the 1991 AIME examination

5. Nine unused problems from the 1987 International Olympiad

6. Two problems from the 1988 USA Olympiad

7. From the 1988 International Olympiad

8. A geometric gem of Duane DeTemple

9. A Kiev Olympiad problem

10. Some student favorites

11. Four unused problems from the 1988 International Olympiad

12. From the 1988 AIME examination

13. An unused Bulgarian problem on the medial *** and the

Gergonne ***

14. Two soluti*** by John Morvay from the 1982 Leningrad High

School Olympiad

15. Two soluti*** by Ed Doolittle

16. From the 1987 Spanish Olympiad

17. A problem from Johann Walter

18. From the 1987 Balkan Olympiad

19. From various Kurschak competiti***

20. Two questi*** from the 1986 National Junior High School

Mathematics competition of the People's Republic of China

21. From the 1986 Spanish Olympiad

22. A geometric c***truction

23. An inequality involving logarithms

24. On isosceles right-angled pedal ***s

25. Two problems from the 1987 Austrian Olympiad

26. From the 1988 Canadian Olympiad

27. A problem on closed sets

28. From the 1987 Austrian-Polish team competition

29. An engaging property concerning the incircle of a

***

30. On floors and ceilings

31. Two problems from the 1987 International Olympiad

32. On arithmetic progressi***

33. A property of ***s having an angle of 30 degrees

34. From the 1985 Bulgarian Spring competition

35. An unused International Olympiad problem from Britain

36. A Romanian Olympiad proposal

37. From the 1984 Bulgarian Olympiad

38. Two Erd?s problems

39. From the 1985 Bulgarian Olympiad

40. From a Chinese contest

41. A Japanese temple geometry problem

42. Two problems from the Second Balkan Olympiad, 1985

43. A property of pedal ***s

44. Three more soluti*** Ge***e Evagelopoulos

45. The power mean inequality

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书籍介绍

Ross H***berger's love of mathematics comes through very clearly in From Erdös to Kiev. He presents intriguing, stimulating problems that can be solved with elementary mathematical techniques. It will give pleasure to motivated students and their teachers, but it will also appeal to anyone who enjoys a mathematical challenge. Most of the problems in the collection have appeared on national or international Olympiads or other contests. Thus, they are quite challenging (with soluti*** that are all the more rewarding). The soluti*** use straightforward arguments from elementary mathematics (often not very technical arguments) with only the occasional foray into sophisticated or advanced ideas. Anyone familia***ith elementary mathematics can appreciate a large part of the book. The problems included in this collection are taken from geometry, number theory, probability, and combinatorics. Soluti*** to the problems are included.